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We consider the hyperbolic version of three-dimensional anisotropicNaver-Stokes equations in a thin strip and its hydrostatic limit that is ahyperbolic Prandtl type equations. We prove the global-in-time existence anduniqueness for the two systems and the hydrostatic limit when the initial databelong to the Gevrey function space with index 2. The proof is based on adirect energy method by observing the damping effect in the systems.

3D hyperbolic Navier-Stokes equations in a thin strip: global well-posedness and hydrostatic limit in Gevrey space